SECR can fit an inhomogeneous Poisson model to describe the distribution of animals. This may be viewed as a surface of expected density across the study area.

The log likelihood is evaluated in `secr.fit`

by summing values at
points on a ‘habitat mask’. Each point in a habitat mask represents a
grid cell of potentially occupied habitat (their combined area may be
almost any shape and may include disjunct patches).

The density model may take one of two forms: a user-provided **R** function
or a linear model on the link scale (see the `link`

argument of
`secr.fit`

; the default link for density is
‘log’). User-provided functions are described in the accompanying
vignette
secr-densitysurfaces.pdf. Here
we focus on linear models.

The full design matrix for density (D) has one row for each point in the mask. The design matrix has one column for the intercept (constant) term and one for each predictor. Predictors may be based on Cartesian coordinates (e.g. ‘x’ for an east-west trend), a continuous habitat variable (e.g. vegetation cover) or a categorical (factor) habitat variable. Predictors must be known for all points in the mask (non-habitat excluded). The variables ‘x’, ‘y’, ‘x2’, ‘y2’, ‘xy’, ‘session’, ‘Session’ and ‘g’ are provided automatically. Other covariates should be named columns in the ‘covariates’ attribute of the habitat mask.

Variable | Description | Data source |

x | x-coordinate | automatic |

y | y-coordinate | automatic |

x2 | x-coordinate^2 | automatic |

y2 | y-coordinate^2 | automatic |

xy | x-coordinate * y-coordinate | automatic |

session | session factor | automatic |

Session | session number 0:(R-1) | automatic |

g | group factor | automatic |

[user] | mask covariate | covariates(mask) as named in formula |

The submodel for density (D) is a named component of the list used in
the `model`

argument of `secr.fit`

. It is expressed in **R**
formula notation by appending terms to *\~*.

Density surfaces resulting from the fitting of SECR models are manipulated in secr as objects of class ‘Dsurface’. See the vignette secr-densitysurfaces.pdf for details and examples, including functions for prediction and plotting.

Note that no density model is fitted when `secr.fit`

is called with
CL = TRUE.

Borchers, D. L. and Efford, M. G. (2008) Spatially explicit maximum
likelihood methods for capture–recapture studies. *Biometrics*
**64**, 377–385.

`secr models`

,
`secr detection models`

,
`secr.fit`

,
`Dsurface`

,
`predictDsurface`

,
`plot.Dsurface`

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